Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element ...Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori er- ror estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the esti- mates for boundary element errors. The theoretical analysis and numerical examples show that the hyper- singular residuals are good a posteriori error indicators in many adaptive boundary element computations.展开更多
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
基金Supported by the National Key Basic Research and Development(973) Program of China (No. G19990328) and the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori er- ror estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the esti- mates for boundary element errors. The theoretical analysis and numerical examples show that the hyper- singular residuals are good a posteriori error indicators in many adaptive boundary element computations.
